Dimension de Heitmann des treillis distributifs et des anneaux commutatifs
Commutative Algebra
2022-01-19 v3
Abstract
We study a notion of dimension which was introduced by R. Heitmann in his remarkable paper in 1984, and also a related notion, implicit in the proofs in his paper. We develop these notions in the general framework of distributive lattices and spectral spaces. We obtain in this way constructive versions of important theorems in commutative algebra, with simpler proofs than the classical ones, and some new results.
Keywords
Cite
@article{arxiv.1712.01958,
title = {Dimension de Heitmann des treillis distributifs et des anneaux commutatifs},
author = {Thierry Coquand and Henri Lombardi and Claude Quitté},
journal= {arXiv preprint arXiv:1712.01958},
year = {2022}
}
Comments
in French, Version corrig\'ee: Janvier 2022. Article original: Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et Th\'eorie des Nombres.(2006), pages 57--100